Urn I and urn II each have two red chips and two white chips. Two chips are drawn simultaneously from each urn. Let X1 be he number of red chips in the first sample and X2 be the number of red chips in the second sample. Find the pdf of X1 + X2.
solution: 0: 1/36, 1: 2/9, 2: 1/2, 3: 2/9, 4: 1/36.
can someone help me understand this problem
Best Answer
The draw from each urn is two red with probability $\frac 16$, because to get two red you need to star with a red (probability $\frac 12$) and then get the other red (probability $\frac 13)$. Similarly, you get two white with probability $\frac 16$, so you get one of each with probability $\frac 23$. Now to get four reds you need to get two reds out of each urn. If you want two of each you have a number of ways to get there-add them up.